The investigation was launched after violence broke out in the King's Cross area, the Seasiders having drawn 3-3 at Wolverhampton Wanderers and the Eagles securing a late 2-1 victory at Peterborough United.
The arrests come on the day the rival clubs are due to meet each other in the league, at Palace's Selhurst Park.
Police enforced crowd control measures when the two played each other in Croydon in January, including holding some fans in the ground after the final whistle to ease the risk of confrontation between rival supporters.
More top news
Wednesday morning's weather for the west of the region
Wednesday morning's weather for the east of the region
Tuesday night's forecast for the west of the region